| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 40 | |
| Number of page(s) | 28 | |
| DOI | https://doi.org/10.1051/cocv/2019024 | |
| Published online | 30 June 2020 | |
Calibrations for minimal networks in a covering space setting
1
Institut für Mathematik, Karl-Franzens-Universität,
Heinrichstrasse 36,
8010
Graz, Austria.
2
Dipartimento di Matematica, Università di Pisa,
Largo Bruno Pontecorvo 5,
56127
Pisa, Italy.
* Corresponding author: marcello.carioni@uni-graz.at
Received:
15
September
2018
Accepted:
10
April
2019
In this paper, we define a notion of calibration for an approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover, we introduce the notion of calibration in families: the idea is to divide the set of competitors in a suitable way, defining an appropriate (and weaker) notion of calibration. Then, calibrating the candidate minimizers in each family and comparing their perimeter, it is possible to find the minimizers of the minimization problem. Thanks to this procedure we prove the minimality of the Steiner configurations spanning the vertices of a regular hexagon and of a regular pentagon.
Mathematics Subject Classification: 49Q20 / 49Q05 / 57M10
Key words: Minimal partitions / Steiner problem / covering spaces / calibrations
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.